One of the most common vectoring schemes is based on linear manipulation of transmission signals across communication lines on the service provider (“network”) side. This is generally referred to as linear precoding. One of the most common schemes for setting coefficients in linear precoding is the zero-forcing approach. This approach is based on the inversion of the channel matrix. The downside of this approach is high performance loss in cases where the far end cross-talk (FEXT) level is considered high. As FEXT level increases with frequency, it is common that performance loss increases as well. To illustrate an example of this phenomenon, reference is made to FIG. 1, which is a bar graph representing an example comparison of prior art performance between the bitrate per single line versus multi-line with precoding for 20 twisted-wire pairs of 300 meters in cable length. The vertical axis in the bar graph of FIG. 1 represents the bitrate in Mbps, while the horizontal axis represents the number of communication lines. It can be noted that:                There is a large difference (gap) between the possible bitrate when each line is active alone and the case where all the lines are active (and precoding is enabled).        The variation between the achievable bitrate per line is very high.        
Various prior art methods exist to further improve performance of linear precoding, however, these methods may be considered of limited benefit for “inferior” communication lines where the cross-talk level is considered high. Furthermore, these prior art methods typically endeavor to maximize a bitrate sum over all communication lines in the vectored group. This may not be consistent with the service provider's business model or commitment of service to the end user. The service provider is typically committed to provide a certain level of service throughput (e.g., bitrate). As such, the service provider may be interested in exceeding a committed service bitrate threshold. Bitrates below this threshold signify that the end user is not receiving the assured service, whereas bitrates above this threshold do not generally contribute any additional revenues to the service provider.
An alternative prior art precoding method is non-linear precoding, based for example on the Tomlinson-Hiroshima precoding (THP) modulo scheme. Although the bitrate losses with the THP modulo scheme due to high FEXT scenarios are lower (compared with linear precoding), still the bitrate variation between the different communication lines may still be of concern. THP (similarly with linear precoding) attempts to maximize the bitrates of different communication lines, with no effort to improve individual communication lines considered to be “inferior”.